. 2021 Apr 19;7(4):e06786. doi: 10.1016/j.heliyon.2021.e06786

Table 3.

Description of landscape pattern metrics and ecological effect metrics used in this study.

	Index	Equation	Ecological significance
Landscape pattern metrics	Compactness index (CI) (Ye et al., 2012)	$C I = \sqrt{\sum_{i = 1}^{n} S_{i} / \sum_{i = 1}^{n} P_{i}}$ where, S_i and P_i are the area and perimeter of patch i, respectively. n is the total number of urban patches in the study area.	The larger the CI value, the more compact the land space pattern.
	Patch density (PD) (Chen and Fu, 1996)	$P D = n / A$ where, A is the total urban area, n is same as above.	PD is the opposite of CI.
	Mean shape index (MSI) (Tian et al., 2003)	$M S I = \frac{\sum_{i = 1}^{n} \frac{P_{i}}{4 \sqrt{S_{i}}}}{n}$	A larger MSI value indicates the space form is less coherent and the land space pattern is more dispersed.
Ecological effect metrics	Value of Ecological Service (VES) (Hou and Qiao, 2012)	$V E S = \sum_{j = 1}^{m} V_{j} S_{j}$ where V_j and S_j are the VES of land use type j per unit area, and area of land use type j, respectively. m is the total number of land use types in the study area, with m = 1 (urban type) in this study. V_j (10000 Yuan/km²) for urban, farmland, forest, grassland, water body, and unused land are 0, 6, 19, 64, 542, and 3.71.
	Ecological elasticity (ECO) (Xu et al., 2010)	$E C O = \sum_{j = 1}^{m} r_{j} e_{j}$ where r_j and e_j are the area ratio of land type j to the total study area and elasticity value of land type j, respectively. The values of e_j for urban, farmland, forest, grassland, water body, and unused land are 0.4, 0.5, 0.9, 0.6, 0.8 and 0.3.	The ability of the ecosystem to return to its original state after disturbance. A higher ECO value indicates the ecosystem is more stable. ECO ranges from 0 to 1.
	Ecological risk index (ERI) (Zhou et al., 2014)	$E R I = \sum_{j = 1}^{m} \frac{S_{j} ω_{j}}{A_{0}}$ where S_j is the area of land use type j, A₀ is the sample area, A₀ = 5 km × 5 km in this study, ω_j is ecological risk intensity of land used type j, the values of ω_j for urban, farmland, forestland, grassland, water body are 0.29, 0.13, 0.03, 0.05 and 0.04.	The lower ERI value, the better for ecosystem. ERI value ranges from 0 to 1.